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FA-54991 / Astronomical coordinate conventions / Open access

Linear spectral pixel calibration: Spectral calibration evaluates at absolute pixel instead of reference displacement · case 01

The adapter reports an incorrect coordinate while other fields remain valid.

Verified by executionVariant 1 · 6 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Spectral calibration evaluates at absolute pixel instead of reference displacement. Faulty expression: d['a']+d['b']*d['p']+d['c']*d['p']**2+d['e']*d['p']**3

VERIFIED REPAIR

Preserve the declared model convention at this site: d['a']+d['b']*(d['p']-d['r'])+d['c']*(d['p']-d['r'])**2+d['e']*(d['p']-d['r'])**3

Unsuccessful approach: A partial convention repair still uses d['a']+d['b']*(d['p']-d['r'])+d['c']*(d['p']-d['r'])**2

Case contract

Spectral coordinate is a reference-centered cubic in one-based pixel displacement t=p-r. Report coordinate, local derivative, reference-independent absolute constant, and the three coefficients after a shift of reference by s. This is a finite exact calibration polynomial, not a dispersion solution. Output fields are defined by: coordinate = d['a']+d['b']*(d['p']-d['r'])+d['c']*(d['p']-d['r'])**2+d['e']*(d['p']-d['r'])**3; local_dispersion = d['b']+2*d['c']*(d['p']-d['r'])+3*d['e']*(d['p']-d['r'])**2; absolute_constant = d['a']-d['b']*d['r']+d['c']*d['r']**2-d['e']*d['r']**3; shifted_zero = d['a']+d['b']*d['s']+d['c']*d['s']**2+d['e']*d['s']**3; shifted_linear = d['b']+2*d['c']*d['s']+3*d['e']*d['s']**2; shifted_quadratic = d['c']+3*d['e']*d['s']

Why this case matters

Catalog, detector, sky-coordinate, and spectroscopy adapters must preserve the association between numeric coordinates and their declared reference conventions.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'coordinate': d['a']+d['b']*d['p']+d['c']*d['p']**2+d['e']*d['p']**3, 'local_dispersion': d['b']+2*d['c']*(d['p']-d['r'])+3*d['e']*(d['p']-d['r'])**2, 'absolute_constant': d['a']-d['b']*d['r']+d['c']*d['r']**2-d['e']*d['r']**3, 'shifted_zero': d['a']+d['b']*d['s']+d['c']*d['s']**2+d['e']*d['s']**3, 'shifted_linear': d['b']+2*d['c']*d['s']+3*d['e']*d['s']**2, 'shifted_quadratic': d['c']+3*d['e']*d['s']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 220, 'local_dispersion': 74, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 220, 'local_dispersion': 74, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 108, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 3, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 100, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 7, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 200, 'local_dispersion': 69, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': 76, 'local_dispersion': -30, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 2: [({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 310, 'local_dispersion': 107, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 310, 'local_dispersion': 107, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 110, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 4, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 106, 'local_dispersion': 11, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 8, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 285, 'local_dispersion': 102, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': 35, 'local_dispersion': -53, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 3: [({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 436, 'local_dispersion': 146, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 436, 'local_dispersion': 146, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 112, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 5, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 124, 'local_dispersion': 26, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 9, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 406, 'local_dispersion': 141, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': -32, 'local_dispersion': -82, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 4: [({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 604, 'local_dispersion': 191, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 604, 'local_dispersion': 191, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 114, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 6, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 160, 'local_dispersion': 47, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 10, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 569, 'local_dispersion': 186, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': -131, 'local_dispersion': -117, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 5: [({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 820, 'local_dispersion': 242, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 820, 'local_dispersion': 242, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 116, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 220, 'local_dispersion': 74, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 11, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 780, 'local_dispersion': 237, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': -268, 'local_dispersion': -158, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
astronomical fixture 0{'absolute_constant': 94, 'coordinate': 604, 'local_dispersion': 74, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}{'absolute_constant': 94, 'coordinate': 220, 'local_dispersion': 74, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}Failed
astronomical fixture 1{'absolute_constant': 94, 'coordinate': 604, 'local_dispersion': 74, 'shifted_linear': 2, 'shifted_quadratic': 3, 'shifted_zero': 100}{'absolute_constant': 94, 'coordinate': 220, 'local_dispersion': 74, 'shifted_linear': 2, 'shifted_quadratic': 3, 'shifted_zero': 100}Failed
astronomical fixture 2{'absolute_constant': 94, 'coordinate': 114, 'local_dispersion': 2, 'shifted_linear': 2, 'shifted_quadratic': 0, 'shifted_zero': 104}{'absolute_constant': 94, 'coordinate': 108, 'local_dispersion': 2, 'shifted_linear': 2, 'shifted_quadratic': 0, 'shifted_zero': 104}Failed
astronomical fixture 3{'absolute_constant': 94, 'coordinate': 160, 'local_dispersion': 2, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}{'absolute_constant': 94, 'coordinate': 100, 'local_dispersion': 2, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}Failed
astronomical fixture 4{'absolute_constant': 109, 'coordinate': 569, 'local_dispersion': 69, 'shifted_linear': -3, 'shifted_quadratic': -3, 'shifted_zero': 110}{'absolute_constant': 109, 'coordinate': 200, 'local_dispersion': 69, 'shifted_linear': -3, 'shifted_quadratic': -3, 'shifted_zero': 110}Failed
astronomical fixture 5{'absolute_constant': 139, 'coordinate': -131, 'local_dispersion': -30, 'shifted_linear': -2, 'shifted_quadratic': -4, 'shifted_zero': 104}{'absolute_constant': 139, 'coordinate': 76, 'local_dispersion': -30, 'shifted_linear': -2, 'shifted_quadratic': -4, 'shifted_zero': 104}Failed

SHA-256 / 294d955c940c3edd319f95eb7d9a4ffa0b4d75ebfcdb7acc3d6631e2e7f23992

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'coordinate': d['a']+d['b']*(d['p']-d['r'])+d['c']*(d['p']-d['r'])**2, 'local_dispersion': d['b']+2*d['c']*(d['p']-d['r'])+3*d['e']*(d['p']-d['r'])**2, 'absolute_constant': d['a']-d['b']*d['r']+d['c']*d['r']**2-d['e']*d['r']**3, 'shifted_zero': d['a']+d['b']*d['s']+d['c']*d['s']**2+d['e']*d['s']**3, 'shifted_linear': d['b']+2*d['c']*d['s']+3*d['e']*d['s']**2, 'shifted_quadratic': d['c']+3*d['e']*d['s']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 220, 'local_dispersion': 74, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 220, 'local_dispersion': 74, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 108, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 3, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 100, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 7, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 200, 'local_dispersion': 69, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': 76, 'local_dispersion': -30, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 2: [({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 310, 'local_dispersion': 107, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 310, 'local_dispersion': 107, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 110, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 4, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 106, 'local_dispersion': 11, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 8, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 285, 'local_dispersion': 102, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': 35, 'local_dispersion': -53, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 3: [({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 436, 'local_dispersion': 146, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 436, 'local_dispersion': 146, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 112, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 5, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 124, 'local_dispersion': 26, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 9, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 406, 'local_dispersion': 141, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': -32, 'local_dispersion': -82, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 4: [({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 604, 'local_dispersion': 191, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 604, 'local_dispersion': 191, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 114, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 6, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 160, 'local_dispersion': 47, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 10, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 569, 'local_dispersion': 186, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': -131, 'local_dispersion': -117, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 5: [({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 820, 'local_dispersion': 242, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 820, 'local_dispersion': 242, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 116, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 220, 'local_dispersion': 74, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 11, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 780, 'local_dispersion': 237, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': -268, 'local_dispersion': -158, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
astronomical fixture 0{'absolute_constant': 94, 'coordinate': 156, 'local_dispersion': 74, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}{'absolute_constant': 94, 'coordinate': 220, 'local_dispersion': 74, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}Failed
astronomical fixture 1{'absolute_constant': 94, 'coordinate': 156, 'local_dispersion': 74, 'shifted_linear': 2, 'shifted_quadratic': 3, 'shifted_zero': 100}{'absolute_constant': 94, 'coordinate': 220, 'local_dispersion': 74, 'shifted_linear': 2, 'shifted_quadratic': 3, 'shifted_zero': 100}Failed
astronomical fixture 2{'absolute_constant': 94, 'coordinate': 108, 'local_dispersion': 2, 'shifted_linear': 2, 'shifted_quadratic': 0, 'shifted_zero': 104}{'absolute_constant': 94, 'coordinate': 108, 'local_dispersion': 2, 'shifted_linear': 2, 'shifted_quadratic': 0, 'shifted_zero': 104}Passed
astronomical fixture 3{'absolute_constant': 94, 'coordinate': 100, 'local_dispersion': 2, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}{'absolute_constant': 94, 'coordinate': 100, 'local_dispersion': 2, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}Passed
astronomical fixture 4{'absolute_constant': 109, 'coordinate': 136, 'local_dispersion': 69, 'shifted_linear': -3, 'shifted_quadratic': -3, 'shifted_zero': 110}{'absolute_constant': 109, 'coordinate': 200, 'local_dispersion': 69, 'shifted_linear': -3, 'shifted_quadratic': -3, 'shifted_zero': 110}Failed
astronomical fixture 5{'absolute_constant': 139, 'coordinate': 140, 'local_dispersion': -30, 'shifted_linear': -2, 'shifted_quadratic': -4, 'shifted_zero': 104}{'absolute_constant': 139, 'coordinate': 76, 'local_dispersion': -30, 'shifted_linear': -2, 'shifted_quadratic': -4, 'shifted_zero': 104}Failed

SHA-256 / ee7bb0f5f4b004a42e6d7c4b2859c8829ddcd150aec73238ffd74e84e64a1827

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(d):
    return {'coordinate': d['a']+d['b']*(d['p']-d['r'])+d['c']*(d['p']-d['r'])**2+d['e']*(d['p']-d['r'])**3, 'local_dispersion': d['b']+2*d['c']*(d['p']-d['r'])+3*d['e']*(d['p']-d['r'])**2, 'absolute_constant': d['a']-d['b']*d['r']+d['c']*d['r']**2-d['e']*d['r']**3, 'shifted_zero': d['a']+d['b']*d['s']+d['c']*d['s']**2+d['e']*d['s']**3, 'shifted_linear': d['b']+2*d['c']*d['s']+3*d['e']*d['s']**2, 'shifted_quadratic': d['c']+3*d['e']*d['s']}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = {1: [({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 220, 'local_dispersion': 74, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 220, 'local_dispersion': 74, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 108, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 3, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 100, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 7, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 200, 'local_dispersion': 69, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': 76, 'local_dispersion': -30, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 2: [({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 310, 'local_dispersion': 107, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 310, 'local_dispersion': 107, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 110, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 4, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 106, 'local_dispersion': 11, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 8, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 285, 'local_dispersion': 102, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 8, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': 35, 'local_dispersion': -53, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 3: [({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 436, 'local_dispersion': 146, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 436, 'local_dispersion': 146, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 112, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 5, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 124, 'local_dispersion': 26, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 9, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 406, 'local_dispersion': 141, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 9, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': -32, 'local_dispersion': -82, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 4: [({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 604, 'local_dispersion': 191, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 604, 'local_dispersion': 191, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 114, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 6, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 160, 'local_dispersion': 47, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 10, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 569, 'local_dispersion': 186, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 10, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': -131, 'local_dispersion': -117, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})], 5: [({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 820, 'local_dispersion': 242, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 0}, {'coordinate': 820, 'local_dispersion': 242, 'absolute_constant': 94, 'shifted_zero': 100, 'shifted_linear': 2, 'shifted_quadratic': 3}), ({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 0, 'e': 0, 's': 2}, {'coordinate': 116, 'local_dispersion': 2, 'absolute_constant': 94, 'shifted_zero': 104, 'shifted_linear': 2, 'shifted_quadratic': 0}), ({'p': 7, 'r': 3, 'a': 100, 'b': 2, 'c': 3, 'e': 1, 's': 2}, {'coordinate': 220, 'local_dispersion': 74, 'absolute_constant': 94, 'shifted_zero': 124, 'shifted_linear': 26, 'shifted_quadratic': 9}), ({'p': 11, 'r': 3, 'a': 100, 'b': -3, 'c': 3, 'e': 1, 's': -2}, {'coordinate': 780, 'local_dispersion': 237, 'absolute_constant': 109, 'shifted_zero': 110, 'shifted_linear': -3, 'shifted_quadratic': -3}), ({'p': 11, 'r': 3, 'a': 100, 'b': 2, 'c': 2, 'e': -1, 's': 2}, {'coordinate': -268, 'local_dispersion': -158, 'absolute_constant': 139, 'shifted_zero': 104, 'shifted_linear': -2, 'shifted_quadratic': -4})]}
for i, (record, expected) in enumerate(fixtures[N]):
    check('astronomical fixture %s' % i, solve(record), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
astronomical fixture 0{'absolute_constant': 94, 'coordinate': 220, 'local_dispersion': 74, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}{'absolute_constant': 94, 'coordinate': 220, 'local_dispersion': 74, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}Passed
astronomical fixture 1{'absolute_constant': 94, 'coordinate': 220, 'local_dispersion': 74, 'shifted_linear': 2, 'shifted_quadratic': 3, 'shifted_zero': 100}{'absolute_constant': 94, 'coordinate': 220, 'local_dispersion': 74, 'shifted_linear': 2, 'shifted_quadratic': 3, 'shifted_zero': 100}Passed
astronomical fixture 2{'absolute_constant': 94, 'coordinate': 108, 'local_dispersion': 2, 'shifted_linear': 2, 'shifted_quadratic': 0, 'shifted_zero': 104}{'absolute_constant': 94, 'coordinate': 108, 'local_dispersion': 2, 'shifted_linear': 2, 'shifted_quadratic': 0, 'shifted_zero': 104}Passed
astronomical fixture 3{'absolute_constant': 94, 'coordinate': 100, 'local_dispersion': 2, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}{'absolute_constant': 94, 'coordinate': 100, 'local_dispersion': 2, 'shifted_linear': 26, 'shifted_quadratic': 9, 'shifted_zero': 124}Passed
astronomical fixture 4{'absolute_constant': 109, 'coordinate': 200, 'local_dispersion': 69, 'shifted_linear': -3, 'shifted_quadratic': -3, 'shifted_zero': 110}{'absolute_constant': 109, 'coordinate': 200, 'local_dispersion': 69, 'shifted_linear': -3, 'shifted_quadratic': -3, 'shifted_zero': 110}Passed
astronomical fixture 5{'absolute_constant': 139, 'coordinate': 76, 'local_dispersion': -30, 'shifted_linear': -2, 'shifted_quadratic': -4, 'shifted_zero': 104}{'absolute_constant': 139, 'coordinate': 76, 'local_dispersion': -30, 'shifted_linear': -2, 'shifted_quadratic': -4, 'shifted_zero': 104}Passed

SHA-256 / 26045dbc2561e4c12cd9a12b76b41474ea6cf78ff08bec2b8189ce3a19bde8df

Verification & scope

Explicitly stipulated finite algebraic adapter; no standards conformance, physical accuracy, or production-library claim. Inputs are the documented finite valid model domain. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:45:53.462647+00:00.

Case digest / a3a24e34dc71b8a9b54bffdfcb61ab4d1936b07f4b9ea6696ba4b28c01986202